Rate Law and Reaction Rate Calculator
Calculate reaction rate using rate = k[A]^m[B]^n.
Find how doubling a concentration affects rate for 0th, 1st, and 2nd order reactions.
The rate law expresses how reaction rate depends on the concentration of reactants.
General rate law:
rate = k × [A]^m × [B]^n
Where:
- k = rate constant (units depend on overall order)
- [A], [B] = molar concentrations (mol/L)
- m, n = individual reaction orders (experimentally determined, usually 0, 1, or 2)
- Overall order = m + n
Effect of doubling a concentration:
| Order | Rate changes by |
|---|---|
| 0 | No change (rate = k) |
| 1 | Doubles (2¹ = 2×) |
| 2 | Quadruples (2² = 4×) |
Units of rate constant k:
| Overall order | Units of k |
|---|---|
| 0 | mol L⁻¹ s⁻¹ |
| 1 | s⁻¹ |
| 2 | L mol⁻¹ s⁻¹ |
| 3 | L² mol⁻² s⁻¹ |
Determining reaction order experimentally: Use the method of initial rates: compare how rate changes as concentration changes.
If doubling [A] doubles the rate → first order in A. If doubling [A] quadruples the rate → second order in A. If doubling [A] has no effect → zero order in A.
Example: For 2NO(g) + O₂(g) → 2NO₂(g): Rate = k[NO]²[O₂] — second order in NO, first order in O₂, third order overall. At [NO] = 0.01 M, [O₂] = 0.01 M, k = 7×10⁹ L²/mol²/s: Rate = 7×10⁹ × (0.01)² × (0.01) = 7×10³ mol/L/s
Where the exponents come from
This is the single most common mistake with rate laws: the orders m and n are not the coefficients from the balanced equation. They are measured. A reaction written 2NO + O₂ → 2NO₂ happens to be second order in NO, but that agreement is a coincidence of its mechanism, not a rule. Plenty of reactions are first order in a species that appears with a coefficient of 3, or zero order in a reactant that is essential to the equation.
Orders are found by the method of initial rates: hold every concentration constant except one, double that one, and see what the rate does. Double the rate means first order in that species, quadruple means second order, no change means zero order. Fractional and negative orders both exist and both point at a multi-step mechanism.
Why the units of k keep changing
The rate constant has whatever units make the equation balance, and those depend on the overall order. For an overall first-order reaction k is in s⁻¹; second order it is L/(mol·s); third order L²/(mol²·s). The pattern is M^(1−order)·s⁻¹.
This is genuinely useful rather than pedantic. If someone hands you a rate constant with units of L/(mol·s), you know without being told that the overall order is 2.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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